Four-Step Block Method for Solving Third Order Ordinary Differential Equation

2018 ◽  
Vol 57 (5) ◽  
pp. 331-344
Author(s):  
K. O. La wal ◽  
◽  
Y. A. Yah aya ◽  
S. D. Yak ubu
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Block Method ◽  
Third Order ◽  
Order Ordinary Differential Equation

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

scholarly journals A Functionally-Fitted Block Numerov Method for Solving Second-Order Initial-Value Problems with Oscillatory Solutions

2021 ◽  
Vol 18 (6) ◽  
Author(s):  
R. I. Abdulganiy ◽  
Higinio Ramos ◽  
O. A. Akinfenwa ◽  
S. A. Okunuga
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Second Order ◽  
Initial Value ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Oscillatory Solutions ◽  
Type Method ◽  
Convergent Method

AbstractA functionally-fitted Numerov-type method is developed for the numerical solution of second-order initial-value problems with oscillatory solutions. The basis functions are considered among trigonometric and hyperbolic ones. The characteristics of the method are studied, particularly, it is shown that it has a third order of convergence for the general second-order ordinary differential equation, $$y''=f \left( x,y,y' \right) $$ y ′ ′ = f x , y , y ′ , it is a fourth order convergent method for the special second-order ordinary differential equation, $$y''=f \left( x,y\right) $$ y ′ ′ = f x , y . Comparison with other methods in the literature, even of higher order, shows the good performance of the proposed method.

scholarly journals Conservation laws for a Boussinesq equation.

2017 ◽  
Vol 2 (2) ◽  
pp. 465-472 ◽  
Author(s):  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Conservation Laws ◽  
Boussinesq Equation ◽  
Point Of View ◽  
Multiplier Method ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Generalized Boussinesq Equation ◽  
The Relationship

AbstractIn this work, we study a generalized Boussinesq equation from the point of view of the Lie theory. We determine all the low-order conservation laws by using the multiplier method. Taking into account the relationship between symmetries and conservation laws and applying the multiplier method to a reduced ordinary differential equation, we obtain directly a second order ordinary differential equation and two third order ordinary differential equations.

scholarly journals New Modified Adomin Decomp osition Metho d for Boundary Value Problems of Higher-order Ordinary Differential Equation

2020 ◽  
pp. 20-37
Author(s):  
Zainab Ali Ab du Al-Rabahi ◽  
Yahya Qaid Hasan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Operator ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Inverse Operator ◽  
Higher Order ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Solving Equations

This study will present a new modified differential operator for solving third-order boundary value problems into higher-order ordinary differential equation. We found the differential operator for new three inverse operator which can be applied for solving equations at more than one type in different conditions. We put a detailed plan for five non-linear examples from a high-order, we get dynamic and quickly to the exact solution.

scholarly journals A New Special 15-Step Block Method for Solving General Fourth Order Ordinary Differential Equations

2021 ◽  
pp. 308-333
Author(s):  
Victor Oboni Atabo ◽  
Solomon Ortwer Adee
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solution ◽  
Fourth Order ◽  
Recent Literature ◽  
New Method ◽  
Block Method ◽  
Order Ordinary Differential Equation ◽  
Direct Numerical Solution ◽  
New Formula

 A new higher-implicit block method for the direct numerical solution of fourth order ordinary differential equation is derived in this research paper. The formulation of the new formula which is 15-step, is achieved through interpolation and collocation techniques. The basic numerical properties of the method such as zero-stability, consistency and A-stability have been examined. Investigation showed that the new method is zero stable, consistent and A-stable, hence convergent. Test examples from recent literature have been used to confirm the accuracy of the new method.

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